Genetic Algorithm Based Tikhonov Regularization Method for Displacement Reconstruction

doi:10.1007/s12204-019-2060-z

Abstract

Abstract: In this paper, a genetic algorithm based Tikhonov regularization method is proposed for determination of globally optimal regularization factor in displacement reconstruction. Optimization mathematic models are built by using the generalized cross-validation (GCV) criterion, L-curve criterion and Engl’s error minimization (EEM) criterion as the objective functions to prevent the regularization factor sinking into the locally optimal solution. The validity of the proposed algorithm is demonstrated through a numerical study of the frame structure model. Additionally, the influence of the noise level and the number of sampling points on the optimal regularization factor is analyzed. The results show that the proposed algorithm improves the robustness of the algorithm effectively, and reconstructs the displacement accurately.

Key words: genetic algorithm| Tikhonov regularization| displacement reconstruction| inverse problem| parameter optimization

摘要： In this paper, a genetic algorithm based Tikhonov regularization method is proposed for determination of globally optimal regularization factor in displacement reconstruction. Optimization mathematic models are built by using the generalized cross-validation (GCV) criterion, L-curve criterion and Engl’s error minimization (EEM) criterion as the objective functions to prevent the regularization factor sinking into the locally optimal solution. The validity of the proposed algorithm is demonstrated through a numerical study of the frame structure model. Additionally, the influence of the noise level and the number of sampling points on the optimal regularization factor is analyzed. The results show that the proposed algorithm improves the robustness of the algorithm effectively, and reconstructs the displacement accurately.

关键词: genetic algorithm| Tikhonov regularization| displacement reconstruction| inverse problem| parameter optimization

CLC Number:

TN 911.7

PENG Zhen (彭真), YANG Zhilong (杨枝龙), TU Jiahuang* (涂佳黄). Genetic Algorithm Based Tikhonov Regularization Method for Displacement Reconstruction[J]. Journal of Shanghai Jiao Tong University (Science), 2019, 24(3): 294-298.

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